Give some cases where it is not possible to determine the inverse of a function.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The inverse of a function f(x) is `f^-1(x)` such that `f(f^-1(x)) = x` . It is not possible to determine the inverse of every function.

If more than one value of x gives the same value for f(x), it would not be possible to determine `f^-1(x)` as it would then be possible for `f^-1(x)` to take on more than one value and it cannot be determined which of them is the correct option.

For example take the function f(x) = x^2. Here f(-x) = f(x) = x^2. The inverse function of f(x) could be equal to `sqrt x` or -`sqrt x`. In such cases it becomes essential to restrict the domain of the function to be able to find the inverse.